The conventional grips of devices such as the grips of the handlebar of a bicycle and the grips of tennis or badminton rackets are commonly spirally wound round with a cover tape for comfortable grasping. Most of the conventional cover tapes have a contact surface made of PU (polyurethane). Such a contact surface is always smooth and does not absorb sweat. Accordingly, such a conventional grip tends to slip from the user's hand when the cover tape is wetted after a long time use. In order to eliminate this problem, the contact surface was roughened by grinding or was embossed by pressure. However, this processing process degrades the structural strength of the PU cover tape, and lowers the elastic material property and shock absorbing ability of the PU cover tape. Further., because the PU cover tape is adhered to the periphery of the grip by means of glue or double-sided adhesive, it tends to be forced out place after long use. Furthermore, because conventional cover tapes for device grip are generally comprised of multiple layers bonded to one another and the surface must be secondarily processed after bonding of the multiple layers, the manufacturing cost of conventional cover tapes for device grip is high.